Structural, Electronic, and Magnetic Properties of Defects in the BC3

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Structural, Electronic, and Magnetic Properties of Defects in the BC3 Sheet from First Principles Yi Ding,†,‡ Yanli Wang,§ and Jun Ni*,† Department of Physics, Key Laboratory of Atomic and Molecular Nanoscience (Ministry of Education), Tsinghua UniVersity, Beijing 100084, People’s Republic of China, Department of Physics, Hangzhou Normal UniVersity, Hangzhou, Zhejiang 310036, People’s Republic of China, and Department of Physics, Center for Optoelectronics Materials and DeVices, Zhejiang Sci-Tech UniVersity, Xiasha College Park, Hangzhou, Zhejiang 310018, People’s Republic of China ReceiVed: January 12, 2010; ReVised Manuscript ReceiVed: June 12, 2010

Using first-principles calculations, we investigate the structures and properties of vacancy and antisite defects in the BC3 sheet. We find that the BC3 sheets with defects show rich electronic and magnetic properties. The vacancies and antisites can cause semiconductor-metal transitions in the BC3 sheet. The magnetism can be induced by mono- and diantisites and divacancies. Formation energies show that antisite defects are more likely formed than vacancy ones in the BC3 sheet. Under suitable chemical potential conditions, the BC3 sheet with defects can become a stable magnetic metal, magnetic semiconductor, and nonmagnetic semiconductor. Our studies demonstrate that the electronic and magnetic properties of the BC3 sheet can be tailored by a defect engineering, which leads to potential applications in the nanoscale electronics and spintronics. Introduction Since the discovery of graphene in 2004, two-dimensional atomic crystals have attracted lots of interest in nanoscience and nanotechnology.1-4 Graphene is a monolayer hexagonal carbon sheet, which is a gapless semimetal with the Dirac-like electronic structure.3,4 By ion irradiations or acid treatments, defects are formed in the graphene sheet and change the electronic properties of graphene.5,6 The atomic defects in the graphene sheet, such as monovacancies and multivacancies, have been observed experimentally by the high-resolution transmission electron microscopy.7 The vacancies can induce magnetism in the graphene sheet and graphene nanoribbons.8-18 Due to the Jahn-Teller distortion, the monovacancy, which is formed by removing one carbon atom from the graphene sheet, is a 5-10 configuration in which two of the three carbon atoms next to the vacancy are bonded to form a pentagon and the other one is left in a concave decagon.11-13 The monovacancy is spinpolarized with a magnetic moment of 1.04 µB, which comes mainly from the unsaturated bonds of the nearest-neighboring carbon atoms to the vacancy.12 When there are several monovacancies in the graphene sheet, the monovacancies are ferromagnetically coupled with those in the same sublattice and antiferromagnetically coupled with those in the different sublattice.14 It makes the total spin of the system depend on its sublattice imbalance, which obeys the Lieb theorem.15,16 When two carbon atoms are removed, the divacancy of a 5-8-5 configuration with two pentagons and one octagon is formed in the graphene sheet.17 The vacancies have strong interactions with atoms and molecules.18,19 In a large supercell calculations (the number of atoms g80), the graphene sheet substituted with B or N atoms are nonmagnetic.18 When CO or N2 molecules * To whom correspondence should be addressed. E-mail: junni@ mail.tsinghua.edu.cn. † Tsinghua University. ‡ Hangzhou Normal University. § Zhejiang Sci-Tech University.

are chemisorbed in the divacancies, the metallic behavior of the graphene sheet is strengthened.19 Boron atoms are normally used as dopants in carbon nanostructures. Mesoporous carbon with homogeneous boron dopants is synthesized and exhibited high capacitance as potential electrode materials for supercapacitors.20 When boron atoms are doped in the zigzag edge, the graphene nanoribbons have intrinsic half-metallic behavior even without an external electric field.21 With the use of an enhanced chemical vapor deposition approach, B-doped single-walled carbon nanotubes can be synthesized in one-step way.22 The theoretical studies show the B-doped single-walled carbon nanotubes can be served as novel chemical sensors for formaldehydes and cyanides.23,24 Using single-walled carbon nanotubes as starting templates, the B-doped single-walled carbon nanotubes with different boron-doping concentrations from 1 to 15 atom % are obtained through the substitution reaction in the experiments.25 High boron-doping concentrations (up to 15 atom %) lead to the formation of BC3 nanotubes instead of a homogeneous random boron substitution in the single-wall carbon nanotubes.26 The corresponding BC3 sheets have also been grown in an epitaxial way on the NbB2 (0001) surface.27-29 Using the free-standing graphene as a membrane to separate two different mediums, the boron atoms can be spontaneously incorporated into the graphene sheets.30 In the experiment, boron carbides with hexagonal-like structures are formed by coevaporation of boron and carbon atoms when the boron content is less than 50%.31 The BC3 sheet and corresponding BC3 nanotubes are semiconductors with gaps of about 0.4-0.6 eV.32-34 First-principles calculations show that the armchair BC3 nanoribbons are all semiconductors, whereas the zigzag BC3 nanoribbons are semiconductors or metals depending on the edge atoms.35 Through step-by-step hydrogenation, the semiconductor-semiconductor-metal transitions may appear in the BC3 sheet.36 However, the properties of defects in the BC3 sheet are not clear. Since vacancy defects affect the magnetic properties of graphene

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Figure 2. Atomic structures and electronic structures of the monovacancies VB (a and c) and VC (b and d) in the BC3 sheet. The shaped regions represents the partial DOSs of the atoms next to the vacancies. The Fermi level is at E ) 0 eV. Figure 1. (a) Structure of the pristine BC3 sheet. (b) The energy bands and DOSs of the pristine BC3 sheet. The 4 × 4 unit cell is delineated by solid lines in panel a. The Fermi level is at E ) 0 eV.

significantly, the defect may also induce magnetism in the BC3 system with only sp electrons. In the boron carbides, the boron (carbon) atoms can substitute the original carbon (boron) atoms to form antisite defects, which may change electronic properties of the boron-carbon systems. Therefore, it is important to make a detailed study on the effects of defects in the BC3 sheet, which can provide insights to tailor the BC3 systems for functional nanostructures. In this work, we preform first-principles calculations to investigate the structural, electronic, and magnetic properties of vacancies and antisites in the BC3 sheet. We find the defects can induce magnetism in the BC3 sheet. The BC3 sheet with defects can become a stable magnetic metal, magnetic semiconductor, and nonmagnetic semiconductor. Methods First-principles calculations are performed by the SIESTA code.37,38 The total energies and electronic structures are calculated within the density functional theory using a double-ζ basis set with additional orbitals of polarization. In our calculations, the Ceperley-Alder exchange-correlation functional of local density approximation is adopted and the Troullier-Martins scheme is used for the norm-conserving pseudopotentials. A grid cutoff of 150 Ry is used, and the Brillouin zone sampling is done by the Monkhorst-Pack method. The k-mesh is set as 3 × 3 × 1 for the relaxations, 5 × 5 × 1 for the static calculations, and 9 × 9 × 1 for gaining the accurate densities of states (DOSs). The supercells are used to simulate the isolated BC3 sheet. The vacuum layer of 12 Å is added in the direction normal to the BC3 sheet, which is large enough to avoid interactions between the periodical images. We use a 4 × 4 unit cell of 128 atoms (shown in Figure 1a) in the calculations, the lattice constant of which is 20.50 Å in the boron-carbon plane. All the structures are relaxed until the maximum atomic forces are smaller than 0.04 eV/Å. The calculations are verified by the VASP code using a plane-wave set and projectoraugmented wave (PAW) pseudopotentials with the exchangecorrelation functional of Perdew-Burke-Ernzerhof (PBE).39,40 The results by the two codes are consistent with each other. The atomic structures and spin charge densities are depicted by XCrySDen.41

Results The pristine BC3 sheet is a semiconductor with a band gap of 0.54 eV. Due to zone folding, the conduction band minimum is moved to the Γ point for a 4 × 4 unit cell as shown in Figure 1b. In the BC3 sheet, the boron atoms are distributed orderly. Carbon hexagons in the boron-carbon plane are linked by boron atoms to each other. The length of C-C bonds is 1.41 Å, which is close to that in the graphene sheet. The B-C bonds in the BC3 sheet are longer than the C-C ones, the length of which is 1.55 Å. These properties agree well with the previous calculations.32,33,35,36 Monovacancies. First, we consider the monovacancies in the BC3 sheet. There are two types of the monovacancies as shown in Figure 2, parts a and b: the monovacancy VB by removing a single boron atom and the monovacancy VC by removing a single carbon atom from the BC3 sheet. For the monovacancy VB, the B-C and C-C bonds near the vacancy are shortened to 1.53 and 1.37 Å, respectively. It causes the carbon atoms to move away from the vacancy, and the distance between them is 2.78 Å, which is larger than that (2.68 Å) of the pristine BC3 sheet. Since the distance is large, there is no Jahn-Teller distortion occurring in the monovacancy. For the monovacancy VC, the B-C and C-C bonds near the vacancy are almost same as those of the pristine BC3 sheet. The nearest-neighboring atoms move toward the vacancy. The distances between these boron and carbon atoms and carbon and carbon atoms are 2.49 and 2.41 Å, respectively, as shown in Figure 2a. They are smaller than those (2.56 and 2.44 Å) in the pristine BC3 sheet. Thus, the area of the monovacancy VC is smaller than that of the monovacancy VB. The electronic properties of the monovacancies VB and VC are much different. From Figure 2, parts c and d, it can be seen that the monovacancy VB leads to a metallic sheet, whereas the BC3 sheet with the monovacancy VC maintains semiconducting properties. This distinction is owing to the different energy levels of the monovacancies. As shown in Figure 2c, the energy levels of the monovacancy VB are high and not located in the band gap of the pristine BC3 sheet. Thus, the extra electrons, which belong to the bonds with the removed atom in the pristine BC3 sheet, fill the conduction bands of the sheet and then the BC3 sheet with the monovacancy VB becomes a metal, whereas for the monovacancy VC, the energy levels are located at about 0.1 eV above the valence band maximum of the pristine BC3 sheet,

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Figure 3. Spin charge densities, energy bands, and DOSs of the monoantisites Canti (a, c, and e) and Banti (b, d, and f) in the BC3 sheet. The Fermi level is at E ) 0 eV.

which reduces the band gap to 0.46 eV. Both the monovacancies VB and VC are nonmagnetic. The large distances of the carbon atoms next to the vacancy prevent the Jahn-Teller distortion in the monovacancies. If the BC3 sheet is rolled into nanotubes, since the curved surfaces decrease these distances, the JahnTeller distortion and spin polarization will occur (see Figure S1 in the Supporting Information). Monoantisites. Now, we investigate the monoantisites in the BC3 sheet. In the monoantisite Canti, one carbon atom substitutes a boron atom in the BC3 sheet. This monoantisite defect can be formed by a carbon atom adsorbed in a monovacancy VB. Likewise, the monoantisite Banti corresponds to a boron atom adsorbed in the monovacancy VC. Parts a and b of Figure 3 show that the deformation of the monoantisites Canti and Banti is relatively smaller than that of monovacancies. For the monoantisite Canti, the antisite carbon has three C-C bonds with the nearest-neighboring carbon atoms. Though these C-C bonds are lengthened to 1.46 Å, the length is still shorter than that of B-C bonds. Thus, the nearby C-C bonds are lengthened to 1.44 Å for the compatible structure as shown in Figure 3a. In the monoantisite Banti, the distance between the antisite boron atom and nearest-neighboring boron atom is enlarged to 1.71 Å. Correspondingly, the antisite boron atom has two short B-C bonds of 1.47 Å with the nearest-neighboring carbon atoms. The length of nearby B-C bonds is also shortened to 1.52 Å, which causes distortions of boron-carbon hexagons as shown in Figure 3b. It is interesting to find that both the monoantisites Canti and Banti are magnetic. By Mulliken population analysis, we find that the pz orbital of the antisite carbon atom is spin-polarized. The antisite carbon atom links three carbon hexagons and forms three C-C σ bonds. Since the pz electrons of the nearestneighboring carbon atoms occupy the delocalized π-orbitals of carbon hexagons, those atoms will not form C-C π bonds with the antisite carbon atom. Thus, there is one unpaired electron left in the pz orbital of the antisite carbon atom, which induces the magnetism in the monoantisite Canti as shown in Figure 3a. Similar to the monovacancy VB, the monoantisite Canti leads to a metallic sheet. As shown in Figure 3c, the Fermi level crosses

Ding et al.

Figure 4. Spin charge densities, energy bands, and DOSs of the divacancy VBC (a, c, and e) and diantisite (BC)anti (b, d, and f) in the BC3 sheet. The Fermi level is at E ) 0 eV.

the pz-character bands. The total magnetic moment is 0.73 µB for the monoantisite Canti. For the monoantisite Banti, an antisite boron atom substitutes one carbon atom in a carbon hexagon. In order to hold the delocalized π-orbital, the extra electrons are needed to fill the pz orbital of the antisite boron atom. Through Mulliken population analysis, we find that the amount of the in-plane s, px, and py electrons of the antisite and nearestneighboring boron atoms is decreased. There are not enough electrons filling in the B-B σ bond of the monoantisite Banti. It causes the spin polarization as shown in Figure 3b. The monoantisite Banti has a total magnetic moment of 1.0 µB and still is a semiconductor. Parts d and f of Figure 3 show the σ-character band of Banti is occupied for one spin and is unoccupied for the other spin, which decreases the band gap to 0.24 eV. Divacancies and Diantisites. From the above results, we can see that there is a close relation between the monovacancies and monoantisites. For the divacancies and corresponding diantisites, their electronic properties are also similar to each other. Figure 4 shows the structures of the divacancy VBC and the corresponding diantisite (BC)anti. For the divacancy VBC, a pair of boron and carbon atoms are removed from the BC3 sheet. Similar to the divacancy in the graphene sheet,17 a reconstruction occurs and the divacancy VBC is a 5-8-5 configuration. However, the two pentagons in the 5-8-5 configuration are unequal. One is a pure carbon pentagon and the other is a hybrid boron carbon pentagon. The distances of the carbon atoms next to the vacancy are different. It is 1.90 Å in the hybrid boron carbon pentagon and much longer than that in the pure carbon pentagon (1.58 Å). The other B-C and C-C bonds are also longer than those of the pristine BC3 sheet, which leads to some distortion of the nearby hexagons. For the diantisite (BC)anti, a pair of boron and carbon atoms are exchanged. The lengths of the bonds in the diantisite are marked in Figure 4b. In comparison to those of pristine BC3 sheet, the B-C bonds are shortened and the C-C bonds are enlarged. Thus, the deformation of the diantisite (BC)anti is small in the BC3 sheet. Both the sheets with the divacancy VBC and diantisite (BC)anti are magnetic metals as shown in Figure 4c-f. The pz orbitals of

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Figure 5. Atomic structures and electronic structures of the divacancy VCC (a and c) and diantisite (BB)anti (b and d) in the BC3 sheet. The shaped regions represents the partial DOSs of the atoms next to the vacancy in panel c and the antisite boron atoms in panel d. The Fermi level is at E ) 0 eV.

carbon atoms in the pure carbon pentagon are spin-polarized. The total magnetic moment is 0.31 µB for the divacancy VBC. Similarly, in the diantisite (BC)anti, the pz orbital of the antisite carbon atom is spin-polarized. The B-C bonds near the antisite boron atoms are also spin-polarized as shown in Figure 4b. The magnetic moment of the diantisite (BC)anti increases to 0.67 µB. The energy levels of the divacancy VBC and diantisite (BC)anti are located in the band gap of the pristine BC3 sheet. Parts c and d of Figure 4 show the Fermi level crosses the bands induced by the defects, which leads to metallic behaviors for the BC3 sheets with the divacancy VBC and diantisite (BC)anti. There is another type of the divacancy formed by removing two nearest-neighboring carbon atoms from the BC3 sheet. The divacancy VCC is shown in Figure 5a, which is also a 5-8-5 configuration as the divacancy VBC. The corresponding diantisite (BB)anti is formed by two boron atoms filling into a divacancy VCC. Since the B-B bonds are longer than the C-C bonds, there is an obvious deformation as shown in Figure 5b. Both the sheets with the divacancy VCC and diantisite (BB)anti are nonmagnetic semiconductors. The divacancy VCC has a similar electronic property to the monovacancy VC. As shown in Figure 5c, the energy levels of the divacancy VCC are located in the band gap of the pristine BC3 sheet, which deceases the band gap to 0.44 eV, whereas for the sheets with the diantisite (BB)anti, Figure 5d shows the electronic property is similar to that of the pristine BC3 sheet. The energy levels of (BB)anti affect the bands of the pristine BC3 sheet slightly. The band gap of the BC3 sheets with the diantisite (BB)anti is changed to 0.53 eV. Discussions of Defect Effects. Table 1 lists the calculated total energies and electronic and magnetic properties of the BC3

sheets with defects. All the defective structures are still planar. There are only the defects of VB and Canti keeping the D3h symmetry, whereas other defects have a lower symmetry of C2V. In order to compare the band structures of the pristine and defective BC3 sheets clearly, we plot the bands along the same high-symmetry lines of the pristine one in Figures 2-5. However, it should be noticed that the high-symmetry lines in the band structures would be different for those defects of C2V symmetry. From Table 1, it can be seen that through replacing atoms by vacancies and antisite atoms, the defects modify the electronic structures of the BC3 sheet significantly. Four rules can be summarized for the defect engineering on the BC3 sheet: (1) Replacing boron atoms by vacancies or carbon atoms leads to semiconductor-metal transitions in the BC3 sheet. (2) When carbon atoms are replaced by vacancies or boron atoms, the values of band gaps are tuned. (3) The magnetism is hard to be induced by the most vacancy defects (only one type of vacancy, VBC, is magnetic). (4) The magnetism can be induced by the most antisite defects (three types of antisites, Banti, Canti, and (BC)anti, are magnetic). The absorption of atoms and molecules on the defects will also tune the properties of the BC3 sheets. For example, we find that through adsorbing on different vacancy defects, one can achieve different magnetic moments of the metal-BC3 systems. When an Fe atom is adsorbed on the VB monovacancy, the system has a magnetic moment of 1.07 µB. When the Fe atom is adsorbed on the VC monovacancy, the system is nonmagnetic. For the VBC divacancy, the Fe atom can be embedded in the BC3 sheet and have a magnetic moment of 4.09 µB. When the Fe atom is embedded in the VCC divacancy, the magnetic moment becomes 3.06 µB. Thus, the chemical modification of defects can be utilized to change further the properties of boron-carbon systems. Stabilities of Defects. In order to apply a defect engineering in the BC3 sheet, the stabilities of vacancies and antisites need to be considered. The formation energy EF is defined as

EF ) Etotal - nBµB - nCµC where Etotal is the total energy of the calculated sheets with defects and nB and nC are the number of boron and carbon atoms, respectively. µB and µC are the chemical potentials of boron and carbon atoms. Under the conditions of low concentrations of defects (about 0.8-1.5% for our supercell calculations), µB and µC refer to the chemical potentials of a defect-free BC3 structure approximately. For the BC3 sheet, the thermodynamic and composition constraints require µB + 3µC ) µBC3. Here µBC3 represents the chemical potential of the BC3 sheet, which is equal to the total energy of the BC3 sheet per BC3 formula unit. Thus,

TABLE 1: Total Energies and Electronic and Magnetic Properties of Vacancies and Antisites in the BC3 Sheeta structure pristine BC3 monovacancy divacancy monoantisite diantisite

sheet VB VC VBC VCC Canti Banti (BC)anti (BB)anti

total energy (eV)

electronic property

magnetic property

-17725.3 -17631.0 -17565.2 -17474.3 -17408.9 -17792.1 -17656.3 -17724.0 -17588.2

semiconductor (0.54 eV) metal semiconductor (0.46 eV) metal semiconductor (0.44 eV) metal semiconductor (0.24 eV) metal semiconductor (0.53 eV)

nonmagnetic nonmagnetic nonmagnetic magnetic (0.31 µB) nonmagnetic magnetic (0.73 µB) magnetic (0.99 µB) magnetic (0.67 µB) nonmagnetic

The total energies of structures are calculated within a 4 × 4 supercell. The value after the semiconductor is the band gap, and the value after the magnetism is the total magnetic moment. a

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Ding et al. defects in the BC3 sheet, the BC3 sheet can become a stable magnetic metal, magnetic semiconductor, and nonmagnetic semiconductor. Our studies demonstrate that the properties of the BC3 sheet can be tuned by a defect engineering, which leads to potential applications as functional nanostructures.

Figure 6. Formation energies EF as functions of µB - µC for defects in the BC3 sheet.

the formation energy with the chemical potential condition of the BC3 sheet can be rewritten as

1 1 EF ) Etotal - (nB + nC)µBC3 - (3nB - nC)(µB - µC) 4 4 Figure 6 shows EF versus µB - µC for different defects. When the EF of a defect is lower than that of the pristine BC3 sheet, the defect is stable and has possibilities to be formed in the sheet. From Figure 6, it can be seen that the monoantisite Canti has the lowest formation energy in the carbon-rich surroundings and the diantisite (BB)anti has the lowest one in the boron-rich surroundings. The monoantisite Banti also has lower formation energy than that of the pristine BC3 sheet under boron-rich conditions, whereas for the vacancy defects, they need extreme boron-rich or carbon-rich conditions to have lower formation energy than the pristine one. Thus, the antisite defects are more likely formed in the BC3 sheet than the vacancy ones. It should be noticed that those total energy calculations are related to 0 K temperature, in which the phonon vibrations and other temperature effects are not considered yet. When the properties listed in Table 1 are combined, the BC3 sheet can become a stable magnetic metal, magnetic semiconductor, and nonmagnetic semiconductor through the defect engineering. Conclusions In summary, we have investigated the structural, electronic, and magnetic properties of vacancies and antisites in the BC3 sheet. The pristine BC3 sheet is a nonmagnetic semiconductor. The defects modify the properties of the BC3 sheets as shown in Table 1. The sheets with the monovacancies VB and VC are nonmagnetic, whereas the sheets with the monoantisites Canti and Banti are magnetic. Both the sheets with the monovacancy VB and corresponding monoantisite Canti are metals, whereas the sheets with the monovacancy VC and corresponding monoantisite Banti maintain semiconducting properties. Due to the spin-polarized C pz orbitals, the sheets with the divacancy VBC and corresponding diantisite (BC)anti are magnetic metals, whereas the sheets with the divacancy VCC and corresponding diantisite (BB)anti are nonmagnetic semiconductors. Rules for the defect engineering have been purposed from the defect effects in the BC3 sheet. The metallic BC3 sheets can be obtained through replacing boron atoms by vacancies or carbon atoms. Replacing carbon atoms by vacancies or boron atoms can tune the band gaps of semiconducting BC3 sheets. The magnetism can be induced by antisite defects in the BC3 sheets. From the formation energies with chemical potential conditions of the BC3 sheet, we find that the antisites are more likely formed than the vacancies in the sheet. By inducing

Acknowledgment. This research was supported by the National Science Foundation of China (Grant Nos. 10974107 and 10721404) and MOST (Grant No. 2006CB605105). Y. Wang also acknowledges the support from Science Foundation of Zhejiang Sci-Tech University (ZSTU) (Grant No. 0913847Y). Parts of the calculations were performed in the Shanghai Supercomputer Center (SSC) of China. Supporting Information Available: Additional figures of the monovacancies in the BC3 nanotubes. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183. (2) Avouris, P.; Chen, Z.; Perebeinos, V. Nat. Nanotechnol. 2007, 2, 605. (3) Neto, A. H. C.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. ReV. Mod. Phys. 2009, 81, 109. (4) Geim, A. K. Science 2009, 324, 1530. (5) Coleman, V. A.; Knut, R.; Karis, O.; Grennberg, H.; Jansson, U.; Quinlan, R.; Holloway, B. C.; Sanyal, B.; Eriksson, O. J. Phys. D: Appl. Phys. 2008, 41, 062001. (6) Tapaszto, L.; Dobrik, G.; Nemes-Incze, P.; Vertesy, G.; Lambin, P.; Biro, L. P. Phys. ReV. B 2008, 78, 233407. (7) Hashimoto, A.; Suenaga, K.; Gloter, A.; Urita, K.; Iijima, S. Nature 2004, 430, 870. (8) Kan, E.; LI, Z.; Yang, J. Nano: Brief Rep. ReV. 2008, 3, 433. (9) Topsakal, M.; Akturk, E.; Sevincli, H.; Ciraci, S. Phys. ReV. B 2008, 78, 235435. (10) Tachikawa, H.; Kawabata, H. J. Phys. Chem. C 2009, 113, 7603. (11) Lehtinen, P. O.; Foster, A. S.; Ma, Y.; Krasheninnikov, A. V.; Nieminen, R. M. Phys. ReV. Lett. 2004, 93, 187202. (12) Ma, Y.; Lehtinen, P. O.; Foster, A. S.; Nieminen, R. M. New J. Phys. 2004, 6, 68. (13) Amara, H.; Latil, S.; Meunier, V.; Lambin, P.; Charlier, J.-C. Phys. ReV. B 2007, 76, 115423. (14) Yazyev, O. V.; Helm, L. Phys. ReV. B 2007, 75, 125408. (15) Palacios, J. J.; Fernandez-Rossier, J.; Brey, L. Phys. ReV. B 2008, 77, 195428. (16) Yazyev, O. V. Phys. ReV. Lett. 2008, 101, 037203. (17) Carlsson, J. M.; Scheffler, M. Phys. ReV. Lett. 2006, 96, 046806. (18) Singh, R.; Kroll, P. J. Phys.: Condens. Matter 2009, 21, 196002. (19) Sanyal, B.; Eriksson, O.; Jansson, U.; Grennberg, H. Phys. ReV. B 2009, 79, 113409. (20) Wang, D.-W.; Li, F.; Chen, Z.-G.; Lu, G. Q.; Cheng, H.-M. Chem. Mater. 2008, 20, 7195. (21) Dutta, S.; Pati, S. K. J. Phys. Chem. B 2008, 112, 1333. (22) Ayala, P.; Plank, W.; Gruneis, A.; Kauppinen, E. I.; Rummeli, M. H.; Kuzmany, H.; Pichler, T. J. Mater. Chem. 2008, 18, 5676. (23) Wang, R.; Zhang, D.; Zhang, Y.; Liu, C. J. Phys. Chem. B 2006, 110, 18267. (24) Zhang, Z.; Zhang, Z.; Liu, C. J. Phys. Chem. B 2006, 110, 4671. (25) Borowiak-Palen, E.; Rummeli, M.; Gemming, T.; Knupfer, M.; Kalenczuk, R.; Pichler, T. Synth. Met. 2005, 153, 345. (26) Fuentes, G. G.; Borowiak-Palen, E.; Knupfer, M.; Pichler, T.; Fink, J.; Wirtz, L.; Rubio, A. Phys. ReV. B 2004, 69, 245403. (27) Yanagisawa, H.; Tanaka, T.; Ishida, Y.; Matsue, M.; Rokuta, E.; Otani, S.; Oshima, C. Phys. ReV. Lett. 2004, 93, 177003. (28) Tanaka, H.; Kawamata, Y.; Simizu, H.; Fujita, T.; Yanagisawa, H.; Otani, S.; Oshima, C. Solid State Commun. 2005, 136, 22. (29) Ueno, A.; Fujita, T.; Matsue, M.; Yanagisawa, H.; Oshima, C.; Patthey, F.; Ploigt, H.-C.; Schneider, W.-D.; Otani, S. Surf. Sci. 2006, 600, 3518. (30) Pontes, R. B.; Fazzio, A.; Dalpian, G. M. Phys. ReV. B 2009, 79, 033412. (31) Caretti, I.; Gago, R.; Albella, J. M.; Jimenez, I. Phys. ReV. B 2008, 77, 174109. (32) Tomanek, D.; Wentzcovitch, R. M.; Louie, S. G.; Cohen, M. L. Phys. ReV. B 1988, 37, 3134. (33) Miyamoto, Y.; Rubio, A.; Louie, S. G.; Cohen, M. L. Phys. ReV. B 1994, 50, 18360.

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